I was there many years ago now (1989 - 1991), so I can't speak to the current state of the seminary. I too studied Classics ... got a double major in Greek and Latin at Loyola University of Chicago, and then completed the graduate coursework in the Patristic Greek and Latin program at The Catholic University of America. I changed course and didn't take the exams, so I never got my Ph.D. (even though I took all the necessary coursework). I was enlisted to teach Latin at the seminary. While at CUA, I also took graduate-level theology courses, and I can say that I learned more theology in the first month at St. Thomas Aquinas than I did at all these classes combined.
I was actually a Freshman at Loyola when I first found an SSPX Mass center and started attending. Then, after my Sophomore year, I decided that I wanted to enter the seminary. So I took summer classes and finished my degrees by the end of my Junior year. After leaving STAS, I eventually returned to grad school at CUA. But I changed course and became a computer programmer (something I had done since the age of 10 on my own) ... to make a living and support my family.
I was there from 2000 - 2003, and I did Bishop Williamson's "zero year" a.k.a. Humanities. So I only made it partway through "third year" even though I spent 7 semesters there.
It was a different place then, and in fact the Winona, MN property is no longer used to train seminarians. The SSPX American seminary is in Virginia now, isn't it?
Different building, different location, different rector, different attitude in the SSPX, different language used to teach theology, different Canon Law taught, different attitude towards the Conciliar hierarchy, different views on the Crisis being taught, etc. (I know you didn't want to get into the Resistance vs. neo-SSPX debate, but frankly it's hard to pass over that element altogether.) There's a reason there's a Resistance -- there are a lot of concrete changes which have taken place, including at the Seminary, and these are the things that many decades-long, non-sedevacantist, serious Catholic, former SSPX supporters are "resisting" at the present day.
I loved my seminary experience, but it's sad to say that it wouldn't be the same today.
I also took to computer programming at a young age (7) but couldn't get my hands on a computer until age 15 -- computers were too expensive back then. Even used computers cost several hundred dollars, and my family was poor at the time. I remember that in 1991, a cheap, slow, crappy computer system (with 14" monitor) used to cost $1,300. There were no "Raspberry Pi" $35 computers, no $300 laptops, no $400 small computers, no $200 little cube computers, none of that.